Unless otherwise indicated herein, the materials described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section.
Communications systems may be designed to operate at error probabilities below a threshold level in order to provide a certain quality of service. In one example, such systems may provide certain quality of service for voice communications when bit error probabilities are below 10−3. In another example, such systems may provide certain quality of service for video communications when block error probabilities are below 10−5.
During the early years of the telecommunications industry, communications providers would typically decrease error probabilities by increasing transmission power. In 1948, Claude Shannon published his work on channel coding theorems and theorized that better error probability to power tradeoffs (i.e., lower error probability using less transmission power) are achievable by implementing error correction codes. Since that time, various error correction coding schemes have been developed that achieve increasingly better error probability to power tradeoffs. However, existing error correction coding schemes may be not be suitable for some modern applications, such as ubiquitous computing systems, satellite communications, and mobile communications.